Broken discs: warp propagation in accretion discs

We simulate the viscous evolution of an accretion disc around a spinning black hole. In general any such disc is misaligned, and warped by the Lense-Thirring effect. Unlike previous studies we use effective viscosities constrained to be consistent with the internal fluid dynamics of the disc. We find that nonlinear fluid effects, which reduce the effective viscosities in warped regions, can promote the breaking of the disc into two distinct planes. This occurs when the Shakura & Sunyaev dimensionless viscosity parameter alpha is <~ 0.3 and the initial angle of misalignment between the disc and hole is >~ 45 degrees. The break can be a long-lived feature, propagating outwards in the disc on the usual alignment timescale, after which the disc is fully co- or counter-aligned with the hole. Such a break in the disc may be significant in systems where we know the inclination of the outer accretion disc to the line of sight, such as some X-ray binaries: the inner disc, and so any jets, may be noticeably misaligned with respect to the orbital plane.

💡 Research Summary

This paper investigates the viscous evolution of a misaligned, thin accretion disc around a spinning black hole, focusing on how Lense‑Thirring precession warps the disc and how the internal fluid dynamics respond. Unlike many earlier works that assume a constant Shakura‑Sunyaev α‑viscosity, the authors adopt the fully non‑linear viscosity prescription derived by Ogilvie (1999), in which the effective viscosities (α₁ for azimuthal shear, α₂ for vertical shear, and α₃ for the coupling term) are functions of the local warp amplitude ψ = |∂ℓ/∂ln R|. As ψ approaches unity, α₂ and α₃ can drop dramatically, weakening the ability of the warped region to transmit shear stresses.

The authors implement a one‑dimensional, axisymmetric disc model that includes the Lense‑Thirring torque T_LT = (2G/c²) J × ℓ / R³. They explore a parameter space with α ranging from 0.1 to 0.4 and initial misalignment angles θ₀ from 10° to 80°. The disc surface density and temperature follow the standard Σ ∝ R⁻³⁄⁴, T ∝ R⁻³⁄⁴ profiles, and the inner boundary allows mass to be accreted onto the black hole while the outer boundary supplies a steady inflow.

The simulations reveal a clear threshold: when α ≲ 0.3 and θ₀ ≳ 45°, the warp becomes sufficiently strong that the non‑linear reduction of α₂ and α₃ essentially shuts off viscous communication across the warped zone. This leads to a “break” in the disc: the inner portion aligns rapidly with the black hole spin (either co‑ or counter‑aligned depending on the exact angle), while the outer portion retains its original orientation. The break propagates outward on a timescale comparable to the usual alignment time (t_align ≈ 1/(αΩ)), but the broken configuration can persist for many viscous times, producing a long‑lived two‑plane structure.

After the break has moved through the disc, the whole disc eventually settles into a single plane, either aligned or anti‑aligned with the spin. The existence of a broken disc has several observational implications. First, the inner disc’s temperature and density profile are altered, potentially producing asymmetric X‑ray line profiles and enhanced variability. Second, because relativistic jets are expected to follow the inner disc’s angular momentum vector, they may be significantly tilted relative to the binary orbital plane or the outer disc that is often inferred from optical observations. This provides a natural explanation for systems where the jet direction appears misaligned with the orbital inclination, such as certain X‑ray binaries.

The study underscores the importance of using a physically consistent, warp‑dependent viscosity rather than a fixed α. It also highlights limitations: the model is one‑dimensional and neglects magnetic fields, radiation pressure, and vertical structure, all of which could modify the break’s longevity and propagation speed. Future work should extend these calculations to full three‑dimensional magnetohydrodynamic simulations and compare the predicted spectral signatures with high‑resolution observations of warped discs and misaligned jets.